1. Field of the Disclosure
The disclosure relates generally to subwavelength-structured composite materials (known as metamaterials) and, more particularly, to techniques for using transmission-line networks to design metamaterials with arbitrary material tensors.
2. Brief Description of Related Technology
The first negative refractive index medium was introduced in the early 2000s and was implemented and tested at microwave frequencies [R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science, vol. 292, pp. 77-79, April 2001]. The work, along with introduction of the “perfect lens” (negative refractive index superlens) by John B. Pendry initiated great interest in subwavelength-structured composite materials possessing tailored electromagnetic properties, materials known today as metamaterials. Soon after these initial experiments, a transmission-line (TL) approach to synthesizing negative refractive index metamaterials was developed [U.S. Pat. No. 6,859,114]. In that TL approach, a host transmission line is periodically loaded with reactive elements. For example, two dimensional isotropic and anisotropic transmission-line metamaterials could be realized that exhibit both negative and positive effective material parameters [Negative Refraction Metamaterials: Fundamental Principles and Applications, G. V. Eleftheriades and K. G. Balmain, Eds. Hoboken, N.J.: Wiley-IEEE Press, 2005]. While metamaterials could be developed, these TL-based metamaterials were limited in that they had diagonal material tensors in the Cartesian basis (a grid aligned with the rectangular unit cell dimensions).
Numerous theoretical devices have been proposed that are designed using transformation optics/electromagnetics [J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science, vol. 312, pp. 1780-1782, June 2006], but few practical realizations have been reported. The few experimental structures reported have either used isotropic metamaterials or metamaterials with contoured unit cells that follow the geometry of the structure, to simplify the required material tensors so that only diagonal tensors are used. For example, in [D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science, vol. 314, pp. 977-980, November 2006.], a cylindrical invisibility cloak was implemented with curved cells which allowed tensor materials that are diagonal in the cylindrical basis to be used. However, if one desires arbitrary control of electromagnetic fields, one must have the ability to design metamaterials with arbitrary material tensors (possessing diagonal and off-diagonal tensor elements). Arbitrary control over the medium in which an electromagnetic field exists translates to arbitrary control over the electromagnetic field itself
There have also been efforts to develop tensor impedance surfaces, which could be used, for example, to convert linearly polarized radiation to circular polarization. The surfaces have been referred to as artificial tensor impedance surfaces and in design contain trapezoidal metallic patches over a metal-backed dielectric substrate. Sievenpiper et al. [Fong, B. H.; Colburn, J. S.; Ottusch, J. J.; Visher, J. L.; Sievenpiper, D. F.; “Scalar and Tensor Holographic Artificial Impedance Surfaces,” Antennas and Propagation, IEEE Transactions on, vol. 58, no. 10, pp. 3212-3221, October 2010] have used parametric studies to form a database of metallic patch geometries and their corresponding surface impedance tensors. This cataloging, however, can be time consuming since no clear relationship between geometry and impedance tensor has been identified. In addition, methods of extending the technique to other frequency regimes have not been proposed.